Soil heat flux and air temperature as factors of radon

NUKLEONIKA 2016;61(3):231237
doi: 10.1515/nuka-2016-0039
ORIGINAL PAPER
Soil heat flux and air temperature
as factors of radon (Rn-222) concentration
in the near-ground air layer
Agnieszka Podstawczyńska,
Włodzimierz Pawlak
Abstract. A unique, highly time-resolved, and synchronous three-year dataset of near-surface atmospheric
radon-222 as well as soil heat flux and air temperature measurements at two sites (rural and urban) in Central
Poland are investigated. The recognition of temporal variability of Rn-222 and selected meteorological variables
in the urban and rural areas served to create two statistical models for estimation of this radionuclide concentration at 2 m a.g.l. The description of the relationships between the variables for individual months was established
on the basis of an exponential function and an exponential function with time derivative of predictor to account
for the hysteresis issue. The model with time derivative provided better results. The weakest fitting of modelled
data to empirical ones is observed for the winter months. During subsequent seasons, air temperature as well
as QG-driven (soil heat flux) models exhibited very high agreement with the empirical data (MBE, RMSE,
MAE, and ‘index of agreement’ by Willmott were used to evaluate the models). A restriction in the use of QG
for Rn-222 concentration was observed only in winter in the case of snow cover occurrence, which reduces the
daily QG variability.
Key words: air temperature • Central Poland • exponential function • Rn-222 • soil heat flux
Introduction
A. Podstawczyńska, W. Pawlak
Department of Meteorology and Climatology,
University of Lodz,
88 Narutowicza Str., 90-139 Lodz, Poland,
Tel.: +48 42 665 5959, Fax: +48 42 665 5951,
E-mail: [email protected], [email protected]
Received: 13 January 2016
Accepted: 18 March 2016
Radon (Rn-222), a radioactive gas with a half-life of 3.82 days, is emitted naturally (0.72–1.2
atoms·cm−2·s−1) from ice-free, unsaturated terrestrial surfaces [1, 2]. The Rn-222 concentration in
the near-surface air layer is undoubtedly strongly
influenced by local conditions, which are connected
with the environment of the gas emissions to the
atmosphere (inter alia: geological formation, soil
characteristics – radium content, permeability and
porosity, temperature vertical profile, soil heat flux,
and humidity) and microclimatic conditions occurring in the near-ground air layer [3]. Research on
Rn-222 in the context of meteorology dates back to
the 1920s [4] and has developed intensively since
the 1960s. In most publications, Rn-222 has been
used to study the atmosphere as a natural tracer of
the processes of transport and dispersion of gases
[5–11]. Rn-222 has also been used as an indicator
of vertical mixing processes resulting in the atmospheric stability regime [12–17]. The temporal variability of the Rn-222 concentration with reference to
the meteorological variables (such as wind velocity
and direction, atmospheric pressure, air tempera-
232
ture, precipitation, and snow cover occurrence) was
presented in the studies by [17–24].
Although Rn-222 research in the meteorological
context has a long tradition, highly time-resolved,
long-term, and synchronous measurements of near-ground atmospheric Rn-222 concentrations in
different environments (inter alia: urban and rural
areas with microclimate diversity) are not very common. In addition, statistical models for the estimation of Rn-222 concentrations in the near-surface air
layer based on the meteorological variables are not
well-documented in literature. Notably, the relationship between the atmospheric Rn-222 concentration
and soil heat flux is poorly understood.
Soil heat flux as a component of the heat balance
of the active surface (ground surface) indirectly
characterizes the thermal properties of the substrate, which are important for the intensity of soil
gas flow into the atmosphere. The sign and value of
QG reflect the temperature differences between the
surface and the deeper layers of the soil [25, 26].
Therefore, this element may give an overview of the
microclimate in the near-ground air layer, indicating the degree of heating or cooling of the earth’s
surface; it may also be an indicator of the Rn-222
exhalation rate. The positive values of QG are a
factor in soil gas migration to the surface of the
earth, theoretically intensifying the Rn-222 exhalation into the atmosphere. The negative values of QG
occur as a consequence of the inverse temperature
profile of the substrate soil, which inhibit the transport of gases to the surface of the earth [27, 28].
The main goal of this study was to evaluate
two meteorological variables, soil heat flux and
air temperature, as predictors of the air Rn-222 concentration variability in the near-surface air layer.
The partial objectives were: (i) recognition of the
temporal variability of the Rn-222 concentration
with reference to selected meteorological elements
and assessment of the statistical relationships between the variables, (ii) creation of statistical mod-
A. Podstawczyńska, W. Pawlak
els for estimation of the Rn-222 air concentrations
based on the soil heat flux and air temperature, (iii)
validation of the models for particular months, and
(iv) comparison of modelled Rn-222 data based on
the soil heat flux and air temperature values.
Data and methods
The study area comprised two sites with different
microclimatic conditions – the centre of Łódź (typical urban station, 51°46'10''N, 19°27'55''E, 214 m
a.s.l.) and a rural, agrarian area in Ciosny village
(25 km north of Łódź, 51°55'24'' N, 19°24'38'' E,
150 m a.s.l.). At the Łódź and Ciosny stations,
continuous synchronous measurements of the radon (Rn-222) concentrations were conducted in
the years 2008–2010, using an ionization chamber
AlphaGUARD®PQ2000PRO (Saphymo GmbH) in
the diffusion mode (averaging time: hour) placed
in a meteorological box 2 m above the ground.
The air temperature (t) was measured using
AlphaGUARD®PQ2000PRO and the soil heat flux
(QG) was measured by means of HFP01 Heat Flux
Plate, Campbell Scientific Ltd. The plates for the
measurements of heat flux in the soil were placed
at a depth of approximately 10 cm. The surrounding land area was covered with grass at both the
measuring stations. The heat flow was expressed
in [W·m–2]. Positive QG means heat flowing to
the surface and negative QG is the propagation of
heat from the surface of the active agent into the
soil. The soil heat flux observations are logged by
CR10X Campbell Scientific, Inc. as 10-min averages
of 10-second readings and subsequently integrated
into hourly averages for analysis.
The exponential function (model I) and the exponential function with time derivative of predictor
to account for the hysteresis issue (model II) were
selected, including but not limited to polynomial
and power functions, to describe the relationship
Fig. 1. Average hourly Rn-222 concentration as a function of soil heat flux (QG) and air temperature (t) for each month
in Ciosny in 2008–2010 (dependence of average daily profiles). The lines mark the regression curves for consecutive
months (model II with time derivative).
Soil heat flux and air temperature as factors of radon (Rn-222) concentration...
233
Fig. 2. Average hourly Rn-222 concentration as a function of soil heat flux (QG) and air temperature (t) for each month
in Łódź in 2008–2010 (dependence of average daily profiles). The lines mark the regression curves for consecutive
months (model II with time derivative).
the between monthly average hourly values of the
Rn-222 concentrations and the meteorological variables. Estimates of the Rn-222 concentrations were
performed for individual months due to the fact that
the diurnal variability of the Rn-222 concentrations
throughout the year was very high. The hysteresis
effect was demonstrated in the form of a loop in the
correlation plots of the Rn-222 concentration and
QG and t, particularly evident in the months from
April to October (Figs. 1 and 2).
The following are the statistical models of dependence of the Rn-222 concentration on heat flux or
temperature, used in the study:
Model I (t2m): Rn = a1 · exp(a2 · t2m) + a3
Model I (QG): Rn = a1 · exp(a2 · QG) + a3
Model II (t2m): Rn = a1 · exp(a2 · t2m) + a3
+ a4(t2m/t)
Model II (QG): Rn = a1 · exp(a2 · QG) + a3
+ a4(QG/t)
where, t2m – air temperature at 2 m a.g.l.
The function parameters were chosen using the
method of least squares so that they describe the experimental results of the Rn-222 concentration most
accurately. The fit of the data obtained using the
presented models to the empirical values was evaluated based on the following fit statistics: systematic
error (MBE), mean square error of measurement
(RMSE), mean absolute error (MAE), and the index
of agreement by Willmott (d) [29, 30]. The index of
agreement (d) varies between 0.0 and 1.0, where a
value of 1.0 expresses perfect agreement between O
(observed values) and P (modelled values), and 0.0
describes complete disagreement.
Following are the fit statistics used in the study:
1) Mean bias error,
N
MBE  N 1   Pi  Oi  
 P  O
i
i
 P i  Oi
N
N
i 1
i
i
2) Root mean square error of measurement
2 0.5
 1 N

RMSE   N   Pi  Oi  
i 1


3) Mean absolute error
N
MAE  N 1  Pi  Oi
i 1
4) The index of agreement by Willmott
2 
 N
   Pi  Oi  
, 0  d  1
d  1   Ni 1
2




P
O


i
i
 

i 1
where: N – number of cases, O – observed values,
–
–
P – modelled values. P = Pi – O, O = Oi – O, where
–
O – average value.
The expression in the denominator is referred to
as the error potential (PE), and the expression in the
numerator is the mean square error of measurement
(MSE) [30]. Willmott’s index of agreement d is a more
accurate fit statistic than those commonly used, that
is, the correlation coefficient R and the coefficient of
determination R2, which are applied for linear models.
For more details concerning the area of investigation, instrumentation and data processing, see the
following papers: [17, 24].
Results
The soil heat flux (QG) and air temperature (t), as
compared with the other meteorological variables
(e.g., soil heat flux, soil humidity, air temperature
in the layer 0.2–2.0 m a.g.l., wind speed, and atmospheric pressure) are characterized by a clear
234
A. Podstawczyńska, W. Pawlak
Fig. 3. Average Rn-222 concentrations depending on air temperature and soil heat flux (QG) in Łódź and Ciosny in
2008–2010 (based on the mean monthly hourly values).
diurnal cycle and the strongest statistical relationships with the atmospheric Rn-222 concentrations
[24]. For this reason, QG and t were used to create
a statistical model for the estimation of the Rn-222
concentrations at 2 m a.g.l. The daily profile of the
Rn-222 concentration represents an inversion of
the air temperature profile, and it varies approximately in phase with the soil heat flux. In Ciosny,
the highest monthly average Rn-222 concentration
was observed at a temperature range of 10–15°C,
whereas for the urban areas, this range was 5–10°C.
The highest monthly average concentrations of
Rn-222 were recorded at QG > 5 W·m–2 and the lowest at QG < –10 W·m–2 at both sites (Figs. 1, 2, and 3).
Still, extreme concentrations of the radionuclide
near the ground occur with some delay as compared
to the minima and maxima of the meteorological
variables. This hysteresis effect, whose physical rea-
son is the inertia of the physical system, was taken
into account in the prediction model II of Rn-222
levels at both stations.
An analysis of the temporal variability of the
Rn-222 concentrations indicated a lack of clear
diurnal cycles from January to March at both the
urban and rural stations (Figs. 4 and 5). In this
season of the year, there are two important factors
determining the atmospheric Rn-222 levels: (i) the
intense dilution processes of atmospheric mixing
due to an increased frequency of cyclonic weather
with strong winds and (ii) the snow cover weakening
the exhalation process. The average daily amplitude
of the Rn-222 concentrations at the stations begins
to increase in April with a maximum in June (Ciosny – 11 Bq·m–3) and September in Łódź (3 Bq·m–3)
(Figs. 4 and 5). The morning increase of the Rn-222
concentrations outside the city is distinctly higher
Fig. 4. Monthly average daily profiles of Rn-222 concentrations in Ciosny in 2008–2010 – the measured and modelled
data on the basis of soil heat flux (QG) and air temperature (t).
Soil heat flux and air temperature as factors of radon (Rn-222) concentration...
235
Fig. 5. Monthly average daily profiles of Rn-222 concentrations in Łódź in 2008–2010 – the measured and modelled
data on the basis of soil heat flux (QG) and air temperature (t).
than in Łódź in all seasons except winter, which
originates from the urban-rural difference in the
diurnal evolution of the atmospheric boundary layer.
The air temperature as well as the soil heat flux-driven models exhibited very high agreement with
the empirical data, especially from April to October.
The index of agreement by Wilmott varied from
0.524 to 0.989 in Łódź and from 0.944 to 0.990
in Ciosny during this period. The models Rn(QG)
and Rn(t) with time derivative (model II) provided
slightly better results in all months of the year than
model I (Figs. 4 and 5). A restricted use of QG for
the prediction of the Rn-222 concentrations was
observed only in winter in the case of snow cover
occurrence, which reduces the daily QG variability
(e.g., February, November in Łódź, Fig. 5).
An analysis of the values of fit statistics (d, MBE,
RMSE, and MAE) confirmed that the choice of the
regression models was good. Inter alia, the systematic error in all cases reached a value close to 0.
The values of the coefficients of determination
calculated for the experimental and modelled values
of the Rn-222 concentrations indicated that the
measured Rn-222 levels at the rural station Ciosny
reflected slightly better the model data than those
from the urban station in the city centre of Łódź
(Figs. 6 and 7). In Łodź, models I and II based on
the air temperature have given better results (R2:
Fig. 6. Experimental and modelled values of Rn-222 concentrations from soil heat flux (QG) and air temperature
(t) in Ciosny in 2008–2010 (calculations were based on
the average daily values).
236
A. Podstawczyńska, W. Pawlak
this variable as a predictor of the atmospheric
Rn-222 levels.
7. The soil heat flux and air temperature could be
used as complementary predictors of the Rn-222
concentration in the near-surface air layer. The
index of agreement by Willmott indicated both
the meteorological variables as good predictors
of the Rn-222 concentration in the near-surface
air layer.
Acknowledgments. Funding for this research was partially provided by the Polish Ministry of Science and
Higher Education under grant N306 015 32/1011. We
would like to express our gratitude to our colleagues
from the Institute of Nuclear Physics PAN, Laboratory
of Radiometric Expertise, for their kind cooperation.
Fig. 7. Experimental and modelled values of Rn-222 concentrations from soil heat flux (QG) and air temperature
(t) in Łódź in 2008–2010 (calculations were based on the
average daily values).
0.91, 0.95) than the models based on the soil heat
flux (R2: 0.87, 0.92), but in Ciosny, the accuracy of
both models was the same (Figs. 6 and 7).
Conclusion
An analysis of the three-year data series of the soil
heat flux and air temperature as predictors of the
Rn-222 concentrations at the near-the-ground air
layer at urban and rural areas showed the following
results:
1. The soil heat flux (QG) and air temperature (t),
as compared with other meteorological variables,
have the strongest statistical relationships with
the Rn-222 concentrations in the near-surface
air layer. The hysteresis effect occurred in the
diurnal profiles of the values of Rn-222 and the
selected meteorological variables.
2. An increase in the Rn-222 levels was observed
during positive values of QG in all months of the
year (heat flowing to the surface – usually started
at ~8.00 p.m. and lasted until morning hours),
which could prove the important role of QG as
a factor in soil gas migration to the surface of the
earth, intensifying the Rn-222 exhalation.
3. The exponential function (model I) and exponential function with time derivative of predictor to
account for the hysteresis issue (model II) were
selected to describe the relationship between the
monthly average hourly values of concentrations
of Rn-222 and meteorological variables – QG
and t.
4. The period from April to October was characterized by a good agreement between the observed
and model-predicted values of the Rn-222 concentration.
5. Model II, taking into account the hysteresis effect, provided slightly better results.
6. In winter months, the snow cover occurrence
reduced the daily QG variability and excluded
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